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# About: Random Vectors and Joint Distributions

Module by: Paul E Pfeiffer. E-mail the author

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 Name: Random Vectors and Joint Distributions ID: m23318 Language: English (en) Summary: Often we have more than one random variable. Each can be considered separately, but usually they have some probabilistic ties which must be taken into account when they are considered jointly. We treat the joint case by considering the individual random variables as coordinates of a random vector. We extend the techniques for a single random variable to the multidimensional case. To simplify exposition and to keep calculations manageable, we consider a pair of random variables as coordinates of a two-dimensional random vector. The concepts and results extend directly to any finite number of random variables considered jointly. If the joint distribution for a random vector is known, then the distribution for each of the component random variables may be determined. These are known as marginal distributions. In general, the converse is not true. However, if the component random variables form an independent pair, the treatment in that case shows that the marginals determine the joint distribution. Subject: Mathematics and Statistics Keywords: applied probability, joint distribution, random variables, random vectors License: Creative Commons Attribution License CC-BY 3.0 Authors: Copyright Holders: Maintainers: Latest version: 1.8 (history) First publication date: Apr 16, 2009 12:27 pm -0500 Last revision to module: Sep 18, 2009 1:50 pm -0500

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## Version History

 Version: 1.8 Sep 18, 2009 1:50 pm -0500 by Changes: `added google analytics tracking code` Version: 1.7 Jul 27, 2009 5:37 pm -0500 by Changes: `Summary updated` Version: 1.6 Jul 27, 2009 5:24 pm -0500 by Changes: `Summary added` Version: 1.5 Jul 27, 2009 12:12 pm -0500 by Changes: ```disjoint union fix ``` Version: 1.4 Jun 19, 2009 11:33 am -0500 by Changes: `m-file fixes, supplemental links, metadata updated` Version: 1.3 Jun 9, 2009 5:35 pm -0500 by Changes: `updated links, images and accessibility` Version: 1.2 May 26, 2009 4:44 pm -0500 by Changes: `fixed module names, and updated content structure` Version: 1.1 May 14, 2009 2:56 pm -0500 by Changes: `content`

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### American Chemical Society (ACS) Style Guide:

Pfeiffer, P. Random Vectors and Joint Distributions, OpenStax_CNX Web site. http://cnx.org/content/m23318/1.8/, Sep 18, 2009.

### American Medical Assocation (AMA) Manual of Style:

Pfeiffer P. Random Vectors and Joint Distributions [OpenStax_CNX Web site]. September 18, 2009. Available at: http://cnx.org/content/m23318/1.8/.

### American Psychological Assocation (APA) Publication Manual:

Pfeiffer, P. (2009, September 18). Random Vectors and Joint Distributions. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/m23318/1.8/

### Chicago Manual of Style (Bibliography):

Pfeiffer, Paul. "Random Vectors and Joint Distributions." OpenStax_CNX. September 18, 2009. http://cnx.org/content/m23318/1.8/.

### Chicago Manual of Style (Note):

Paul Pfeiffer, "Random Vectors and Joint Distributions," OpenStax_CNX, September 18, 2009, http://cnx.org/content/m23318/1.8/.

### Chicago Manual of Style (Reference, in Author-Date style):

Pfeiffer, P. 2009. Random Vectors and Joint Distributions. OpenStax_CNX, September 18, 2009. http://cnx.org/content/m23318/1.8/.

### Modern Languages Association (MLA) Style Manual:

Pfeiffer, Paul. Random Vectors and Joint Distributions. OpenStax_CNX. 18 Sep. 2009 <http://cnx.org/content/m23318/1.8/>.